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math.NA2024★ 1 cited
An efficient proximal-based approach for solving nonlocal Allen-Cahn equations
Olena Burkovska, Ilyas Mustapha
In this work, we present an efficient approach for the spatial and temporal discretization of the nonlocal Allen-Cahn equation, which incorporates various double-well potentials an…
math.NA2019
Affine approximation of parametrized kernels and model order reduction for nonlocal and fractional Laplace models
Olena Burkovska, Max Gunzburger
We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius…
math.NA2018★ 7 cited
Regularity and approximation analyses of nonlocal variational equality and inequality problems
Olena Burkovska, Max Gunzburger
We consider linear and obstacle problems driven by a nonlocal integral operator, for which nonlocal interactions are restricted to a ball of finite radius. These type of operators…